THEMATIC PROGRAMS

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Numerical and Computational Challenges in Science and Engineering Program

Graham Gladwell, University of Waterloo

LECTURES

January 18, 2002, 10:30 am

Total Positivity, the QR Algorithm, and Toda Flow

Matrices that appear in physical problems are not arbitrary: they have specified patterns of zero and non-zero terms, and specified patterns of signs. Totally positive, and the related descriptors strictly totally positive, oscillatory, and sign-oscillatory are related to important examples of such sign patterns. It is shown that all these properties remain invariant under shifted QR/RQ transformation, and under Toda flow. This provides important new ways of constructing
isospectral families of matrices for various vibrating systems.



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